Thanks for the fast replies.
This old "trailer" was a gift from my father who'd bought it for like $20. The only time I've ever towed it was to haul a fairly heavy (500 lbs??) gas powered welder from his house to mine. I aired up the old tires, they held

and I trailered home. I looked rough, but towed nice and smooth. No swaying. Aside from the extra load on my little truck's engine I could hardly tell I was pulling something.
As to the "ugly" part....well, I won't be using the whole trailer frame. Just the axle if I can determine what the optimum load for this axle. I have access to a lot of equipment that can make something rusty look fairly nice again.
Let me ask this... Say you have a torsion axle that is rated at 1000 lbs. If the axle is bearing this designated load is there something like a proper deflection angle difference from when it's not loaded? This trailer is jacked up on blocks in my pics, so there is no load on the axle.
Also, to determine if the rubber parts you mentioned are OK, are these type axles able to be disassembled for inspection?